The obtaining and analysis of modified/generalized versions of the
famous Heisenberg uncertainty relation or principle corresponds
to diverse generalizations of the standard Heisenberg algebra (HA)
with basic relation \([X, P] = {\rm i}\hbar \)  for the position
and momentum operators. This direction of research is under development for
more than three decades (with some early works
quoted as [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}),
and still remains to be a hot topic,
see, e.g., [8]}, [9]}, [10]}, [11]}, [12]}, [13]}
for more recent papers.
Physically, deformations of the Heisenberg algebra and the
related generalized uncertainty relation find their motivation
in quantum gravity, in string theory, noncommutative geometry etc.
An overview of different approaches can be found, e.g., in [14]}, [15]}.
What concerns the particular existing variants of deformed Heisenberg algebra (DHA),
we have to note that predominantly there were DHAs with deformed r.h.s. of the basic
relation for \(X\)  and \(P\)  that involved a function of momentum,
or some function of the Hamiltonian. However, within more exotic approach followed
in [2]}, [7]}, deformation of HA emerged in the l.h.s. of basic
relation, by using “\(q\) -commutator” instead of the usual commutator.
